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A POSTERIORI ERROR ESTIMATES FOR APPROXIMATE SOLUTIONS OF ELLIPTIC BOUNDARY VALUE PROBLEMS IN TERMS OF LOCAL NORMS AND OBJECTIVE FUNCTIONALS
- Authors: Muzalevsky A.V.1, Repin S.I.2, Frolov M.E.1
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Affiliations:
- Peter the Great St. Petersburg Polytechnic University
- St. Petersburg Department of the V.A. Steklov Mathematical Institute of the Russian Academy of Sciences
- Issue: Vol 64, No 12 (2024)
- Pages: 2270–2285
- Section: General numerical methods
- URL: https://bakhtiniada.ru/0044-4669/article/view/279978
- DOI: https://doi.org/10.31857/S0044466924120042
- EDN: https://elibrary.ru/KCLPCF
- ID: 279978
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Abstract
Functional relations have been obtained that allow us to evaluate the accuracy of approximate solutions in terms of measures significantly different from the energy norms that are usually used for these purposes. In particular, they are applicable to local norms and measures constructed using specially built linear functionals. The need for such precision control tools arises if there is a special interest in the behavior of the solution in some subdomain or in the special properties of the solution. It is shown that a posteriori functional-type estimates, which were previously used for global estimates, can be adapted to solve this problem. Functional identities and estimates are obtained that allow estimating the error of any conformal approximations in terms of a wide class of measures, including local norms and problem-oriented functionals. The theoretical results are verified in a series of examples that confirm the effectiveness of the proposed method.
About the authors
A. V. Muzalevsky
Peter the Great St. Petersburg Polytechnic UniversitySt. Petersburg, Russia
S. I. Repin
St. Petersburg Department of the V.A. Steklov Mathematical Institute of the Russian Academy of Sciences
Email: repin@pdmi.ras.ru
St. Petersburg, Russia; St. Petersburg, Russia; Peter the Great St. Petersburg Polytechnic University
M. E. Frolov
Peter the Great St. Petersburg Polytechnic UniversitySt. Petersburg, Russia
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